Monitoring - Hall Plots

One of the difficulties in analysing injection well performance is the variation in pressure and injection rate with time. The Hall plot method can be used to eliminate complications due to these variations
This original Hall Plot method is based on Darcy's equation for radial flow from the wellbore. Don't use it. Use the modified Hall plot.
A plot of the cumulative volume injected versus the pressure summation (integration of formation face differential pressure times time) gives what is known as a Hall Plot.
It is a common (but often inappropriate) simplification to plot only cumulative wellhead pressure against cumulative volume. This has the advantage that only variables directly measurable at the surface; wellhead pressure and injection rate, are needed. Don't do this. The slope of the simplified Hall plot is skewed and no longer has a quantitative meaning.
Adjust the available pressure information to bottomhole conditions, by adding on hydrostatic head and subtracting the correct tubing and perforation friction and reservoir pressure. You can use the Well Hydraulics routine in the PWRI Toolbox. The modified Hall plot method is based on plotting the injection pressure potential {the integral of p_bh - p_e with respect to time} against the cumulative injection, W_i. USE THIS. It is the Modified Hall Plot.

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Yes, except that the slope has a different meaning. The inflow can no longer be assumed to be radial and the slope will represent a more complex geometry. From Joshi´s equation for horizontal wells the slope can be derived as (use whichever analytical approximation of horizontal injection that you prefer).
For inclined holes, recognize that there will be a skin component due to deviation?
The Hall plot method is also valid for fractured injectors. You will need to incorporate skin into the radial flow equation for quantification of the effect of the fracture. The Hall plot does offer a means of quantitatively determining skin and changes in skin by manipulating the basic equations.

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Figure 1 illustrates a Modified Hall Plot with several changes in slope accompanied by possible explanations for the well injectivity changes.
In order for slope changes on the Hall Plot to be correctly interpreted the reservoir pressure must be included, i.e. the Modified Hall Plot must be used.

Figure 1. A characteristic modified Hall Plot, showing fluctuations due to the type of fluid (influencing bottomhole formation face pressure and mobility) and an acid treatment. In this case, the slope is governed more by viscosity than by stimulation.
An increase in the slope indicates an accumulation of damage. If skin is calculated from the basic relationships, it will be seen to increase with increasing slope.
A decrease in the slope indicates an improvement in injectivity. If skin is calculated from the basic relationships, it will be seen to decrease with decreasing slope. This could be due to stimulation or to changes in the injected fluid, to a shut-in, to changes in the formation pressure that have not been corrected accounted for, to reductions in the tubing friction (i.e., an acid wash and pickling).

Always. It is simple and the required information for baseline plotting (rate and wellhead pressure) are available.
Convert wellhead pressures to formation face pressure. You can also generate the plot with bottomhole pressure to see if degradation of the injection string is an issue.
Always do your best to use the current best-estimate or measurement of average reservoir pressure.
The Modified Hall Plot may be used as a monitoring tool to identify problem injectors.
It may also be used to evaluate the effectiveness of a stimulation treatment or to compare the effectiveness of several stimulation treatments against one another. This is using an improvement index, which shows the ratio of the II after and before stimulation and - from the date of the stimulation - extrapolates the behavior from immediately after the stimulation forward in time. When deviation from this extrapolation occurs, there is an indication that supplementary stimulation is required.

The Hall plot smooths out local fluctuations in data that are sometimes (usually) apparent in daily plots of the Injectivity Index.
The basic data are usually availalble.
Quantitative interpretation is possible.
It is a continuous monitoring system over a period of time which sometimes can be more representative of trends than single point measurements from a falloff test, for example.

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Like most other monitoring methods, the Hall Plot Method is totally reliant on accurate rate and pressure measurements and a reliable method to convert WHP to BHP. Fiber optics may be the route for the future - although capital expenditures for installation are large.
An estimate of effective reservoir pressure variation over time is required. This may not always be available. In reservoirs with very good connectivity (high permeability homogeneous) the reservoir pressure may be well defined, but in tight reservoirs, it may be more difficult to infer the pressure variation.